Difference in output between numpy linspace and numpy logspace

Question

Numpy linspace returns evenly spaced numbers over a specified interval. Numpy logspace return numbers spaced evenly on a log scale.

I don't understand why numpy logspace often returns values "out of range" from the bounds I set. Take numbers between 0.02 and 2.0:

import numpy as np
print np.linspace(0.02, 2.0, num=20)
print np.logspace(0.02, 2.0, num=20)

The output for the first is:

[ 0.02        0.12421053  0.22842105  0.33263158  0.43684211  0.54105263
  0.64526316  0.74947368  0.85368421  0.95789474  1.06210526  1.16631579
  1.27052632  1.37473684  1.47894737  1.58315789  1.68736842  1.79157895
  1.89578947  2.        ]

That looks correct. However, the output for np.logspace() is wrong:

[   1.04712855    1.33109952    1.69208062    2.15095626    2.73427446
    3.47578281    4.41838095    5.61660244    7.13976982    9.07600522
   11.53732863   14.66613875   18.64345144   23.69937223   30.12640904
   38.29639507   48.68200101   61.88408121   78.6664358   100.        ]

Why does it output 1.047 to 100.0?

Answer 1

2017 update: The numpy 1.12 includes a function that does exactly what the original question asked, i.e. returns a range between two values evenly sampled in log space.

The function is numpy.geomspace

>>> np.geomspace(0.02, 2.0, 20)
array([ 0.02      ,  0.0254855 ,  0.03247553,  0.04138276,  0.05273302,
        0.06719637,  0.08562665,  0.1091119 ,  0.13903856,  0.17717336,
        0.22576758,  0.28768998,  0.36659614,  0.46714429,  0.59527029,
        0.75853804,  0.96658605,  1.23169642,  1.56951994,  2.        ])

Answer 2

logspace computes its start and end points as base**start and base**stop respectively. The base value can be specified, but is 10.0 by default.

For your example you have a start value of 10**0.02 == 1.047 and a stop value of 10**2 == 100.

You could use the following parameters (calculated with np.log10) instead:

>>> np.logspace(np.log10(0.02) , np.log10(2.0) , num=20)
array([ 0.02      ,  0.0254855 ,  0.03247553,  0.04138276,  0.05273302,
        0.06719637,  0.08562665,  0.1091119 ,  0.13903856,  0.17717336,
        0.22576758,  0.28768998,  0.36659614,  0.46714429,  0.59527029,
        0.75853804,  0.96658605,  1.23169642,  1.56951994,  2.        ])

Answer 3

From documentation for numpy.logspace() -

numpy.logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None)

Return numbers spaced evenly on a log scale.

In linear space, the sequence starts at base ** start (base to the power of start) and ends with base ** stop (see endpoint below).

For your case, base is defaulting to 10, so its going from 10 raised to 0.02 to 10 raised to 2 (100).

Answer 4

This is pretty simple.

NumPy gives you numbers evenly distributed in log space.

i.e. 10^(value). where value is evenly spaced between your start and stop values.

You'll note 10^0.02 is 1.04712 ... and 10^2 is 100